Am I missing something here or is the fatigue tests of a return home journey (for example returning to Esgaroth after the first adventure) is somewhat obscene? They are going to rest for a long time in the city anyway so what's the point of making those tests?

Well, it's the adventure of it all. Sure, any fatigue and endurance loss will be negated by a fellowship phase. But they might accumulate shadow, or spend some hope. Also, the test could trigger more adventure adventure along the way. Being jumped by some goblins on the way home, especially after suffering a little fatigue, can make for a memorable homecoming.

Keep in mind that you can always skip it and just say they get home eventually. I just feel that travel should always have some implied risk involved. But if ever there was a time for an easy trip home it would be after a harrowing adventure.

I don't think it will make sense

There's always the risk of hazards, and personally I apply Fatigue during the journey so if the PC fails one roll without a Hazard, then he gets Fatigue that he has to deal with the next time he rolls and maybe does encounter a Hazard.